Because its relative to the sorted permutation (with repetitions) list of the argument. A. does this as well.
A. 1 0 1 A. 0 2 1 1 ----- Original Message ----- From: Raul Miller <[email protected]> To: Programming forum <[email protected]> Sent: Thursday, May 5, 2016 7:25 PM Subject: Re: [Jprogramming] permutation and combination numbers (with repeat) I am not understanding, still. So let's try a different example: Why are these equal? permN 0 0 1 0 1 permN 0 1 0 1 1 permN 1 0 1 1 1 Thanks, -- Raul On Thu, May 5, 2016 at 6:20 PM, 'Pascal Jasmin' via Programming <[email protected]> wrote: > Its relative to the sorted order of the input > > rp1 =: (] (] <@; $:^:(1<#)@del1~)"1 0 ~.@]) > untreep =: (({.,"0 1 $:^:(1<L.)@}.)&>) > rperm6 =: (a: ;"1@(]#~ -.@e."1) ,&.:(<"1)@:untreep@:rp1) > > rperm6 0 0 1 > 0 0 1 > 0 1 0 > 1 0 0 > > > rperm6 0 1 1 > 0 1 1 > 1 0 1 > 1 1 0 > > > > in both cases, the 0 index is the sorted order > > permN 1 0 1 > 1 > permN 1 0 0 > 2 > > the index in their respective permutation lists. > > ----- Original Message ----- > From: Raul Miller <[email protected]> > To: Programming forum <[email protected]> > Sent: Thursday, May 5, 2016 6:13 PM > Subject: Re: [Jprogramming] permutation and combination numbers (with repeat) > > Why are these two results equal? > > permN 0 0 1 > 0 > permN 0 1 1 > 0 > > Thanks, > > -- > Raul > > > On Thu, May 5, 2016 at 5:58 PM, 'Pascal Jasmin' via Programming > <[email protected]> wrote: >> Some routines to calculate permutation and combination numbers, similar to >> A. (but allows permutations with repeat) >> >> del1 =: i.~ ({. , >:@[ }. ]) ] >> >> combN =: (0:`((<:@[ - {.@]) $: >:@{.@] -~ }.@])@.(0 < #@]) + 0:`(<:@#@] >> +/@:! <:@[ - i.@{.@])@.(0 < {.@]) ) >> >> combNF =: 3 : 'a =. 1 { 0 {:: y label_. (i.a) + +/\ 1 {:: ([ (] ;~ [ - 1 ,~ >> _2 >:@{ ]) }:@] , {:@] ([ ({.@] ,(- {:)) ] (] , {~) 1 i:~ >:) (0 , ] >> (+/\)@:! ( a i.@:-~ [) -~ [)/@:<:@[ )&>/^: (<:a) y'@:; >> >> permC =: # %&(x:@:(*/))&:! #/.~ >> >> permN1 =: ((0:`( (] - <./)@:({.@] del1 [) $: (] - <./)@:}.@] )@.(1 < #@])) >> + (permC % #)@] * [ i. {.@] ) f. >> >> permN =: /:~ permN1 ] >> >> 100x combN 15 25 35 45 55 65 85 >> 11284989655 >> >> 100 7 combNF 11284989655x >> 15 25 35 45 55 65 85 >> >> permN 1 0 0 2 1 3 3 1 >> 434 >> >> haven't done the reverse to permN yet, but these routines combined can be >> used to compress any list into 2 numbers (with a key). You can google for >> combinatorial number base, and there is A., but not sure A. has been done >> for permutations with repeats. Which produces smaller numbers than A. does >> (due to fewer underlying permutations). >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
